学术报告

Scaled Relative Graph: a rigorous geometric tool for operators and convergence analysis

发布人:发布时间: 2019-12-30

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题目: Scaled Relative Graph: a rigorous geometric tool for operators and convergence analysis

报告人:印卧涛(UCLA 数学系)

摘要:Many iterative algorithms can be thought of as fixed-point iterations of contractive or nonexpansive operators. Traditionally, such algorithms and operators are analyzed analytically, with inequalities. In this talk, we formalize a correspondence between common operators (such as proximal mapping and subdifferentials of convex functions) and geometric objects on the complex plane. We use elementary Euclidean geometry to rapidly prove many useful results regarding the convergence of fixed-point iterations and their optimal stepsizes. The formalism maps various classes of operators to sets on the complex plane and also maps algebraic operations such as scaling, inversion, addition, and composition of operators to geometric operations on sets on the complex plane. Equipped with these tools, we use geometric arguments to review classic results and obtain two novel convergence results. This talk includes joint work with Ernest Ryu and Robert Hannah (arXiv:1902.09788).

时间:2020年1月2日16:00-17:00

地点:南京大学鼓楼校区西大楼108

报告人简介:

印卧涛,2001年本科毕业于南京大学,2006年哥伦比亚大学毕业,师从Donald Goldfarb, 2006-2013在美国Rice大学计算域应用数学系,先后任讲师、副教授。2013年至今任加州大学(洛杉矶分校)UCLA数学系教授。2016年在华人数学家大会上获得晨兴应用数学金奖,2009年获得Alfred P. Sloan Fellow,2008年获得NSF CAREER Award。研究兴趣:主要是optimization methods and algorithms for large-scale problems。主要研究方向为异步并行计算,一阶方法和优化算子分裂,稀疏优化。

邀请人:杨俊锋 老师